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Today I have purchased some $\ce{HCl(aq)}$ on my local market with a concentration of 23%.
However, I need to obtain a concentration of 37% in order to perform an experiment. Can I use distillation process to increase the acid concentration?
If yes, can I use standard chemistry glassware to process it? (In an isolated system to prevent the $\ce{HCl(g)}$ from escaping of course.)

Distillation unit

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    $\begingroup$ If that experience is you feeling a lot of pain, this would do it. Depending on how much acid you have casually bought, this could be really dangerous. HCl is a gas, if you heat up your little experiment, it will go wherever it pleases, most likely heavily react with your body, you will also breathe it in and it could get into your eyes, making you blind and helpless. Please stop whatever you are doing before people get hurt. $\endgroup$ – AMT Mar 3 '17 at 11:08
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    $\begingroup$ Why not adjust the other reactants in your reaction in order to reach the same concentrations throughout the process? This seems a lot safer. Would you mind sharing with us your procedure? $\endgroup$ – Felipe S. S. Schneider Mar 3 '17 at 12:12
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    $\begingroup$ What experiment are you attempting? 23% HCl strikes me as concentrated enough to do most reactions that call for conc. HCl. $\endgroup$ – Waylander Mar 3 '17 at 12:24
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    $\begingroup$ As sternly warned by users above, there are serious safety issues at play here, so please do your due diligence about precautions and consult an expert if need be. $\endgroup$ – jonsca Mar 4 '17 at 1:43
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    $\begingroup$ you mention using an isolated system, closed glassware apparatuses are seriously dangerous when performing chemical reactions! Your usually heating up something, or the reaction might produce gas by itself. This means your apparatus has to withstand the significant pressure this causes, and it won't do that. The result will be that you're picking out the glass shrapnel from your face while you're lungs are burned by the gaseous HCl you set free. There is no way to perform this reaction safely without a fume hood and expertise. $\endgroup$ – Mad Scientist Mar 4 '17 at 12:23
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Add Calcium Chloride to destroy the azeotrope. Then distill and capture the vapor phase.

See the second method "Extractive Distillation" here:

http://www.jacobs.com/uploadedFiles/wwwjacobscom/20_Learn_About_Us/25_Products/252_Chemetics/Hydrochloric%20Acid%20Concentration.pdf

(Obviously, proper equipment and safety precautions are essential.)

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Irrespective of the potential hazards to an inexperienced chemist attempting distillation of hydrochloric acid, especially absence of adequate safety measures such as a fume hood, in this case, distillation will not result in a higher concentration of acid. Hydrogen chloride and water form a constant-boiling mixture (azeotrope) at ~20% HCl, which is what you are already starting with. I suggest you read the Wikipedia page on Hydrochloric Acid for starters.

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$HCl/H_2O$ forms an azeotrope at atmospheric pressure at ~108.6°C with an $HCl$ concentration of ~20.2%

If you try to distill your 23% mixture, you will outgass a bit of HCl as the mixture heats, thereafter you'll get constant boiling azeotrope. If you bought a pool acid or other commercial HCl mix, distilling this might be a good first step, though. They sometimes put "stabelizer" or a colourant in it and there might be other impurities as well. Also, if you could distill, cooling water would not work to condense HCl in the setup shown in your drawing, as it boils at around -85°C.

You can use $CaCl_2$ or $MgCl_2$ (hygroscopic) to capture some of the water and "break" the azeotrope that way. Take half of your dilute $HCl$ (or as much as you need) and chill it (ice bath), add $CaCl_2$ to the non-chilled half (or however much you need) heat it gently and bubble the captured gas/vapour phase through the chilled dilute $HCl$. Avoid suck-back of the chilled $HCl$ (use a reverse funnel or appropriate setup). You should be able to get up to 37% $HCl$

Please note the safety precautions needed to handle HCl gas. The solution may "foam" when the HCl is bubbled through. HCl has 42% solubility in water at atmospheric pressure and 20°C, but around 37% it will start fuming in moist air.

The second way (wouldn't recommend it): If you have the facilities to do it safely, you could produce $HCl$ gas (as per the old Manheim process) from $NaCl$ and $H_2SO_4$ and then bubble the captured gas through your dilute $HCl$ solution (or through distilled water if you want to be sute of your final product concentration and make sure your final product doesn't have any other contaminants) to make your concentrated $HCl$ (Note: be careful you don't get suck-back of dilute HCl into your hot reagents when doing this, especially if you heat it enough to get the second reaction.)

This is a two-step process that produces HCl at both steps. First an exothermic reaction that will supposedly occur at room temperature, but in practice needs some heat and moisture to get going:

$NaCl + H_2SO_4 → HCl + NaHSO_4$

The second step is endothermic:

$NaCl + NaHSO_4 → HCl + Na_2SO_4$

You have to heat your reagents to high temperatures for the second step.

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